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Remark on the existence results for fractional impulsive integrodifferential equations in Banach spaces. (English) Zbl 1256.34065
Summary: This paper deal with the study of the existence of solutions of nonlinear fractional integrodifferential equations with impulsive conditions in Banach spaces by means of fixed point principle.
MSC:
34K37Functional-differential equations with fractional derivatives
34K30Functional-differential equations in abstract spaces
34K45Functional-differential equations with impulses
47N20Applications of operator theory to differential and integral equations
References:
[1]Agarwal, R. P.; Benchohra, M.; Hamani, S.: A survey on the existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta applicandae mathematicae 109, 973-1033 (2010) · Zbl 1198.26004 · doi:10.1007/s10440-008-9356-6
[2]Balachandran, K.; Kiruthika, S.: Existence of solutions of abstract fractional impulsive semilinear evolution equations, Electron J qual theor differ equat, No. 4, 1-12 (2010) · Zbl 1201.34091 · doi:emis:journals/EJQTDE/2010/201004.pdf
[3]Balachandran, K.; Kiruthika, S.: Existence results for fractional integrodifferential equations with nonlocal condition via resolvent operators, Comput math appl 62, 1350-1358 (2011) · Zbl 1228.34013 · doi:10.1016/j.camwa.2011.05.001
[4]Balachandran, K.; Trujillo, J. J.: The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces, Nonlinear anal: theor methods appl 72, 4587-4593 (2010) · Zbl 1196.34007 · doi:10.1016/j.na.2010.02.035
[5]Balachandran, K.; Kiruthika, S.; Trujillo, J. J.: Existence results for fractional impulsive integrodifferential equations in Banach spaces, Commun nonlinear sci numer simulat 16, 1970-1977 (2011) · Zbl 1221.34215 · doi:10.1016/j.cnsns.2010.08.005
[6]Balachandran, K.; Kiruthika, S.; Trujillo, J. J.: On fractional impulsive equations of Sobolev type with nonlocal condition in Banach spaces, Comput math appl 62, 1157-1165 (2011) · Zbl 1228.34014 · doi:10.1016/j.camwa.2011.03.031
[7]Hilfer, R.: Applications of fractional calculus in physics, (2000)
[8]Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J.: Theory and applications of fractional differential equations, (2006)
[9]Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011